Nonparametric estimation of marginal distributions for unordered pairs

TL;DR

This paper introduces new nonparametric estimators for marginal distributions of unordered pairs, establishing their asymptotic properties and demonstrating their effectiveness through simulations and real data application.

Contribution

The paper proposes novel estimators for unordered pair data and proves their asymptotic properties, filling a gap in nonparametric distribution estimation.

Findings

Establishment of Glivenko-Cantelli theorem for the estimators

Functional central limit theorem proved for the estimators

Successful application to homologous chromosomes data

Abstract

In this article, we consider the estimation of the marginal distributions for pairs of data are recorded, with unobserved order in each pair. New estimators are proposed and their asymptotic properties are established, by proving a Glivenko-Cantelli theorem and a functional central limit result. Results from a simulation study are included and we illustrate the applicability of the method on the homologous chromosomes data.